Humble cleric covering Middle East (6)
I believe the answer is:
demean
'humble' is the definition.
(demeaning is a kind of humbling)
'cleric covering middle east' is the wordplay.
'cleric' becomes 'dean' (I've seen this before).
'covering' indicates putting letters inside.
'middle east' becomes 'me'.
'dean' enclosing 'me' is 'DEMEAN'.
(Other definitions for demean that I've seen before include "Lower in reputation, shame" , "'Put down, degrade (6)'" , "make base" , "Cause (someone) to suffer loss of dignity" , "Lower in status or reputation" .)